Mathematics for 3D Game Programming and Computer Graphics, Second Edition

Book Description
This completely updated second edition illustrates the mathematical concepts that a game programmer would need to develop a professional-quality 3D engine. Although the book is geared toward applications in game development, many of the topics appeal to general interests in 3D graphics. It starts at a fairly basic level in areas such as vector geometry and linear algebra, and then progresses to more advanced topics in 3D game programming such as illumination and visibility determination. Particular attention is given to derivations of key results, ensuring that the reader is not forced to endure gaps in the theory. The book assumes a working knowledge of trigonometry and calculus, but also includes sections that review the important tools used from these disciplines, such as trigonometric identities, differential equations, and Taylor series. Key Features * Includes four new chapters: the graphics pipeline, the stencil shadow rendering technique, curves & surfaces, and numerical methods * Concentrates on key mathematical topics for programming 3D game engines * Discusses applications in the context of the OpenGL architecture due to its cross-platform nature and long-standing industry acceptance. Sample rendering code is presented using ARB vertex programs and fragment programs * Selected topics include quaternions, homogeneous coordinates, ray tracing, bump mapping, portal systems, polygonal techniques, shadows, and physics * Includes exercise sets for use as a textbook New to This Edition The following are selected revisions in the second edition: * A new preliminary chapter that provides a review of the 3D rendering pipeline * A new chapter containing an advanced discussion of the stencil shadow rendering technique * A new chapter covering various numerical methods pertinent to 3D graphics programming, including numerical solutions to linear systems, numerical eigenvalue determination, and numerical integration * A new chapter covering curves and surfaces, including Bézier curves and B-splines * New discussions of texture filtering, mipmapping, and infinite projection matrices * Updated lighting method implementations and collision detection techniques * Additional exercises in all chapters

Book Info
Text concentrates on key mathematical topics for programming 3D game engines and computer graphics. Includes new chapters on the graphics pipeline, the stencil shadow rendering technique, and numerical methods. Includes exercise sets for use as a textbook. Previous edition: c2001. Softcover. DLC: Computer games--Programming.

About the Author
Eric Lengyel (Sunnyvale, CA) is the Chief Technology Officer for the game engine development studio, Terathon Software. He holds an M.S. in mathematics from Virginia Tech and has written several articles for gamasutra.com and the Game Programming Gems series. He is also the author of The OpenGL Extensions Guide.


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Mathematics for 3D Game Programming and Computer Graphics, Second Edition illustrates all the mathematical techniques that software engineers, graphics programmers, and game programmers need to develop a professional-quality 3D engine, and has been completely updated to cover all the recent advancements in 3D graphics technology. In addition to providing all new information on illumination, collision detection, polygonal techniques, and much more, there are four completely new chapters covering the rendering pipeline, shadows, numerical methods, and curves and surfaces. Each chapter includes completely new summaries and exercise sets for additional practice, or for use as a textbook. The book assumes a working knowledge of calculus, trigonometry, and how to use 3D graphics libraries.KEY FEATURES￯﾿ﾽ       Concentrates on key mathematical topics for programming 3D game engines￯﾿ﾽ       Includes four completely new chapters on the rendering pipeline, shadows, numerical methods, and curves and surfaces￯﾿ﾽ       Contains updated information on illumination, collision detection, and polygonal techniques, with new discussions        on bilinear and trilinear texture filtering, infinite projection matrices, and much more￯﾿ﾽ       Includes exercise sets for use as a textbook


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